Multi-antenna techniques can significantly increase the data rates and reliability of a wireless communication system. The performance is particularly improved if both the transmitter and the receiver are equipped with multiple antennas, which results in a multiple-input multiple-output (MIMO) communication channel. Such systems and/or related techniques are commonly referred to as MIMO.
The Long Term Evolution (LTE) communication standard is currently evolving with enhanced MIMO support. A core component in LTE is the support of MIMO antenna deployments and MIMO related techniques. Currently LTE-Advanced supports an 8-layer spatial multiplexing mode for 8 transmit (Tx) antennas with channel dependent precoding. The spatial multiplexing mode is aimed for high data rates in favorable channel conditions. An illustration of the spatial multiplexing operation is shown in FIG. 1. IFFT in FIG. 1 stands for Inverse Fast Fourier Transform and is used for Orthogonal Frequency Division Multiplexing (OFDM).
As seen, the information carrying symbol vector s is multiplied by an NT×r precoder matrix W, which serves to distribute the transmit energy in a subspace of the NT-dimensional vector space. The NT-dimensional vector space corresponds to NT antenna ports. The precoder matrix is typically selected from a codebook of possible precoder matrices, and typically indicated using a precoder matrix indicator (PMI), which specifies a unique precoder matrix in the codebook for a given number of symbol streams. If the precoder matrix is confined to have orthonormal columns, then the design of the codebook of precoder matrices corresponds to a Grassmannian subspace packing problem. The r symbols in s each correspond to a layer and r is referred to as the transmission rank. In this way, spatial multiplexing is achieved, since multiple symbols can be transmitted simultaneously over the same time/frequency resource element (TFRE). The number of symbols r is typically adapted to suit the current channel properties.
LTE uses OFDM in the downlink, and Discrete Fourier Transform (DFT) precoded OFDM in the uplink, and hence, the received NR×1 vector yn for a certain TFRE on subcarrier n (or alternatively data TFRE number n) is modeled byyn=HnWsn+en where en is a noise/interference vector obtained as realizations of a random process. The precoder matrix, W, can be a wideband precoder, which is constant over frequency, or can be frequency selective.
The precoder matrix is often chosen to match the characteristics of the NR×NT MIMO channel matrix H, resulting in so-called channel dependent precoding. This is also commonly referred to as closed-loop precoding and essentially strives for focusing the transmit energy into a subspace which is strong in the sense of conveying much of the transmitted energy to the user equipment (UE). In addition, the precoder matrix may also be selected to strive for orthogonalizing the channel, meaning that after proper linear equalization at the UE, the inter-layer interference is reduced.
In closed-loop precoding for the LTE downlink, the UE transmits, based on channel measurements in the forward link, i.e. the downlink, recommendations to the enhanced NodeB (eNodeB) of a suitable precoder to use. For example, in wideband precoding, a single precoder that is supposed to cover a large bandwidth may be fed back. It may also be beneficial to match the frequency variations of the channel and instead feedback a frequency-selective precoding report, e.g., to report several precoders, one per sub band. This is an example of the more general case of channel state information (CSI) feedback, which also encompasses feeding back other entities than precoders to assist the eNodeB in subsequent transmissions to the UE. Such other information may include channel quality indicators (CQIs) as well as transmission rank indicator (RI).
The transmission rank, and thus the number of spatially multiplexed layers is reflected in the number of columns of the precoder. For efficient performance, it is important that a transmission rank that matches the channel properties is selected.
In the LTE downlink, the UE is reporting CQI and RI and precoders to the eNodeB via a feedback channel. The feedback channel is either on Physical Uplink Control Channel (PUCCH) or on Physical Uplink Shared Channel (PUSCH). The former is a rather narrow bit pipe where CSI feedback is reported in a semi-statically configured and periodic fashion. On the other hand, reporting on PUSCH is dynamically triggered as part of the uplink grant. Thus, the eNodeB can schedule CSI transmissions in a dynamic fashion. In contrast to the PUCCH where the number of physical bits is currently limited to 20, the reports on PUSCH can be considerably larger. Such a division of resources makes sense from the perspective that semi-statically configured resources such as PUCCH cannot adapt to quickly changing traffic conditions, thus making it important to limit their overall resource consumption.
In LTE Rel10, for 8 antenna ports, a factorized precoder structure is used: =W1W2. The first precoder, W1, is a wideband precoder targeting long term channel characteristics and the second precoder, W2, is a frequency-selective precoder targeting short term channel characteristics and differences in polarization. A precoder matrix indicator (PMI) for each of the two precoders is supplied by the UE, choosing each precoder from a limited set of available precoders (codebooks). The PMI reporting for each of the two precoders can be configured with different frequency granularity.
The LTE standard implements a variation of the following factorized precoder. The wideband precoder
      W    1    =      [                            X                          0                                      0                          X                      ]  has a block diagonal structure targeting a uniform linear array (ULA) of N cross-polarized antennas, i.e. the number of antenna ports NT=2N. With this structure, the same N×1 precoder X is applied to each of the two polarizations.
The precoder X is a DFT-based precoder, implementing a Grid-of-Beams codebook, supplying the UE with beams pointing at different directions to choose from. The DFT-based codebook has entries
            X      l        =                  [                                            1                                                      e                                  j                  ⁢                                                                          ⁢                  2                  ⁢                  π                  ⁢                                                            1                      ⁢                      l                                        NQ                                                                                      …                                                      e                                  j                  ⁢                                                                          ⁢                  2                  ⁢                  π                  ⁢                                                                                    (                                                  N                          -                          1                                                )                                            ⁢                      l                                        NQ                                                                                      ]            T        ,l=0, . . . , NQ−1, where Q is an integer oversampling factor, defining the number of beams available in the codebook.
The DFT-based precoders are tailored to a ULA with a specific number of antenna ports. A separate codebook for each number of supported antenna ports NT must then be specified. The frequency-selective precoder for rank 1 is defined as
            W      2        =          [                                    1                                                              e                              j                ⁢                                                                  ⁢                ω                                                        ]        ,            where      ⁢                          ⁢      ω        =                  2        ⁢                                  ⁢        π        ⁢                                  ⁢        p            P        ,p=0, . . . , P−1 and P=4. In this case, the resultant precoder becomes
  W  =                    W        1            ⁢              W        2              =                            [                                                    X                                            0                                                                    0                                            X                                              ]                ⁡                  [                                                    1                                                                                      e                                      j                    ⁢                                                                                  ⁢                    ω                                                                                ]                    =                        [                                                    X                                                                                                          e                                          j                      ⁢                                                                                          ⁢                      ω                                                        ⁢                  X                                                              ]                .            
As seen, W2 targets the phase difference between polarizations. In the LTE standard, the wideband precoder is instead
            W      1        =          [                                                                  X                ~                            l                                            0                                                0                                                              X                ~                            l                                          ]        ,wherein {tilde over (X)}l=[Xl . . . Xl+Nb−1], l=0, . . . , NQ−1, c consists of several precoders from the DFT-based codebook X. W2 is then extended to be a tall matrix comprising selection vectors which selects one of the precoders in {tilde over (X)}l (in addition to changing the phase between polarizations).
A convenient way of extending the DFT-based precoders aimed for ULAs onto two-dimensional antenna arrays is by combining two DFT-based precoders by means of a Kronecker product. The Kronecker product A⊗B between two matrices
  A  =      [                                        A                          1              ,              1                                                …                                      A                          1              ,              M                                                            ⋮                          ⋱                          ⋮                                                  A                          N              ,              1                                                …                                      A                          N              ,              M                                            ]  and B is defined as
            A      ⊗      B        =          [                                                                  A                                  1                  ,                  1                                            ⁢              B                                            …                                                              A                                  1                  ,                  M                                            ⁢              B                                                            ⋮                                ⋱                                ⋮                                                                              A                                  N                  ,                  1                                            ⁢              B                                            …                                                              A                                  N                  ,                  M                                            ⁢              B                                          ]        ,i.e. the matrix B is multiplied to each of the elements of A. The two-dimensional precoder XNVk+l is then formed asXNVk+l=XHk⊗XVl,where XHk is a DFT-based precoder targeting the horizontal dimension, XVl is a DFT-based precoder targeting the vertical dimension, and NV is the number of vertical antenna ports. This has the effect of applying the vertical precoder XVl on each column of the antenna array and the horizontal precoder XHk on each row of the antenna array.
A problem with existing solutions is that a large amount of overhead is caused by PMI reporting which in turn poses a problem on payload limited feedback channels such as periodic PMI reporting on PUCCH.